Forecasting Wind and Solar Power Production
Henrik Madsen (1), Henrik Aalborg Nielsen (2)
Pierre Pinson (1), Peder Bacher (1)
hm@imm.dtu.dk
(1) Tech. Univ. of Denmark (DTU)
DK-2800 Lyngby
www.imm.dtu.dk/˜hm
(2) ENFOR A/S
Lyngsø Allé 3
DK-2970 Hørsholm
www.enfor.dk
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 1
Outline
Some ongoing projects ...
Wind Power Forecasting in Denmark
Methods used for predicting the wind power
Configuration example for a large system
Spatio-temporal forecasting
Use of several providers of MET forecasts
Uncertainty and confidence intervals
Scenario forecasting
Value of wind power forecasts
Solar power forecasting
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 2
Some projects ....
FlexPower (PSO)
iPower (SPIR)
Ensymora (DSF) (wind, solar, heat load, power load, price, natural gas load)
Optimal Spining Reserve (Nordic)
SafeWind (FP7)
AnemosPlus (FP7)
NORSEWind (FP7)
Radar at Sea (PSO)
Mesoscale (PSO)
Integrated Wind Planning Tool (PSO)
Vind i Øresund (Intereg IV)
Solar and Electric Heating in Energy Systems (DSF)
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 3
Wind Power Forecasting in Denmark
WPPT (Wind Power Prediction Tool) is one of the wind power forecasting solutions
available with the longest historie of operational use.
WPPT has been continuously developed since 1993 – initially at DTU (Technical
University of Denmark and since 2006 by ENFOR – in close co-operation with:
Energinet.dk,
Dong Energy,
Vattenfall,
The ANEMOS projects and consortium (since 2002)
DTU (since 2006).
WPPT has been used operationally for predicting wind power in Denmark since 1996.
WPPT (partly as a part of ’The Anemos Wind Power Prediction System’) is now used
in Europe, Australia, and North America.
Now in Denmark (DK1): Wind power covers on average about 26 pct of the system load.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 4
Prediction of wind power
In areas with high penetration of wind power such as the Western part of Denmark and the
Northern part of Germany and Spain, reliable wind power predictions are needed in order to
ensure safe and economic operation of the power system.
Accurate wind power predictions are needed with different prediction horizons in order to
ensure
(a few hours) efficient and safe use of regulation power (spinning reserve) and the
transmission system,
(12 to 36 hours) efficient trading on the Nordic power exchange, NordPool,
(days) optimal operation of eg. large CHP plants.
Predictions of wind power are needed both for the total supply area as well as on a regional
scale and for single wind farms.
Today also reliable methods for ramp forecasting is provided by most of the tools.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 5
Modelling approach – the inputs
Depending on the configuration the forecasting system can take advantage of input from the
following sources:
Online measurements of wind power prod. (updated every 5min. – 1hr).
Online measurements of the available production capacity.
Online “measurements” of downregulated production.
Aggregated high resolution energy readings from all wind turbines in the groups
defined above (updated with a delay of 3-5 weeks).
MET forecasts of wind speed and wind direction covering wind farms and sub-areas
(horizon 0–48(120)hrs updated 2–4 times a day).
Forecasted availability of the wind turbines.
Other measurements/predictions (local wind speed, stability, etc. can be used).
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 6
System characteristics
The total system consisting of wind farms measured online, wind turbines not measured
online and meteorological forecasts will inevitably change over time as:
the population of wind turbines changes,
changes in unmodelled or insufficiently modelled characteristics (important
examples: roughness and dirty blades),
changes in the NWP models.
A wind power prediction system must be able to handle these time-variations in model and
system. WPPT employes adaptive and recursive model estimation to handle this issue.
Following the initial installation WPPT will automatically calibrate the models to the actual
situation.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 7
The power curve model
The wind turbine “power curve” model,
ptur = f (wtur ) is extended to a wind farm
model, pwf = f (wwf , θwf ), by introducing
wind direction dependency. By introducing a
representative area wind speed and direction it
can be further extended to cover all turbines in
an entire region, par = f (w̄ar , θ̄ar ).
HO - Estimated power curve
k
k
P
P
Wind direction
The power curve model is defined as:
Wind direction
Wind speed
k
Wind speed
k
p̂t+k|t = f ( w̄t+k|t , θ̄t+k|t , k )
P
where
w̄t+k|t is forecasted wind speed, and
θ̄t+k|t is forecasted wind direction.
The characteristics of the NWP change with
the prediction horizon. Hence the dependendency of prediction horizon k in the model.
P
Wind direction
Wind speed
Wind direction
Wind speed
Plots of the estimated power curve for
the Hollandsbjerg wind farm (k = 0, 12,
24 and 36 hours).
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 8
The dynamical prediction model
The power curve models are used as input for an adaptively estimated dynamical model,
which (as a simple example) leads to the following k-stop ahead forecasts:
p̂t+k|t
=
3
X
i=1
[cci
a1 pt + a2 pt−1 + b p̂pc
t+k|t +
2iπh24
2iπh24
t+k
t+k
s
cos
+ ci sin
] + m + et+k
24
24
where pt is observed power production, k ∈ [1; 48] (hours) is prediction horizon, p̂pc
t+k|t is
power curve prediction and h24
t+k is time of day.
Model features include
multi-step prediction model to handle non-linearities and unmodelled effects,
the number of terms in the model depends on the prediction horizon,
non-stationarity are handled by adaptive estimation of the model parameters,
the deviation between observed and forecasted diurnal variation is described using
Fourier expansions.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 9
A model for upscaling
The dynamic upscaling model for a region is defined as:
loc
ar
ar
,
k
)
p̂
,
θ̄
=
f
(
w̄
p̂reg
t+k|t
t+k|t
t+k|t
t+k|t
where
p̂loc
t+k|t is a local (dynamic) power prediction within the region,
ar
is forecasted regional wind speed, and
w̄t+k|t
ar
is forecasted regional wind direction.
θ̄t+k|t
The characteristics of the NWP and p̂loc change with the prediction horizon. Hence the
dependendency of prediction horizon k in the model.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 10
Configuration Example
Power Curve
Model
This configuration of WPPT is used by a
large TSO. Characteristics for the installation:
Dynamic
Model
A large number of wind farms and
stand-alone wind turbines.
Online prod.
prediction
Upscaling
Model
Frequent changes in the wind
turbine population.
Offline production data with a
resolution of 15 min. is available
for more than 99% of the wind
turbines in the area.
Online data for a large number
of wind farms are available. The
number of online wind farms increases quite frequently.
Area prod.
prediction
Online prod.
data
NWP data
Total prod.
prediction
Offline prod.
data
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 11
Fluctuations of offshore wind power
Fluctuations at large offshore wind farms have a significant impact on the control and
management strategies of their power output
Focus is given to the minute scale. Thus, the effects related to the turbulent nature of
the wind are smoothed out
When looking at time-series of power production at Horns Rev (160MW/209MW)
and Nysted (165 MW), one observes successive periods with fluctuations of larger
and smaller magnitude
We aim at building models
based on historical wind power
measures only...
... but able to reproduce this
observed behavior
this calls for regime-switching
models
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 12
Results - Horns Rev
MSAR models
generally outperform
the others
1 minute Horns Rev
RMSE [kW]
25
20
15
10
2
4
6
8
10
12
Test data set
5 minute Horns Rev
14
10
12
Test data set
10 minute Horns Rev
14
16
80
60
40
2
4
6
8
16
18
SETAR
MSAR
STAR
ARMA
150
RMSE [kW]
18
SETAR
MSAR
STAR
ARMA
100
20
In the RADAR@sea
project the regime shift
is linked to convective
rain events – which are
detected by a weather
radar.
SETAR
MSAR
STAR
ARMA
30
RMSE [kW]
The evaluation set is
divided in 19 different
periods of different
lengths and
characteristics
100
50
0
2
4
6
8
10
Test data set
12
14
16
18
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 13
Spatio-temporal forecasting
Predictive improvement (measured in
RMSE) of forecasts errors by adding the
spatio-temperal module in WPPT.
23 months (2006-2007)
15 onshore groups
Focus here on 1-hour forecast only
Larger improvements for eastern part
of the region
Needed for reliable ramp forecasting.
The EU project NORSEWinD will
extend the region
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 14
Combined forecasting
In addition to the improved performance also the robustness of the system is increased.
DMI
WPPT
DWD
WPPT
Met Office
WPPT
Comb
Final
7500
C.all
C.hir02.loc.AND.mm5.24.loc
6000
6500
7000
hir02.loc
mm5.24.loc
5500
These could come from parallel
configurations of WPPT using NWP
inputs from different MET
providers or they could come from
other power prediction providers.
RMS (MW)
A number of power forecasts are
weighted together to form a new
improved power forecast.
The example show results achieved for the
Tunø Knob wind farms using combinations
of up to 3 power forecasts.
5
10
15
20
Hours since 00Z
If too many highly correlated forecasts are
combined the performance may decrease
compared to using fewer and less correlated forecasts. Typically an improvement
on 10-15 pct is seen by including more than
one MET provider.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 15
Uncertainty estimation
kW
0
2000
4000
Tunø Knob: Nord Pool horizons (init. 29/06/2003 12:00 (GMT), first 12h not in plan)
12:00
Jun 30 2003
18:00
0:00
6:00
Jul 1 2003
12:00
18:00
0:00
Jul 2 2003
18:00
0:00
Oct 11 2003
18:00
0:00
Oct 13 2003
18:00
0:00
Jul 2 2003
18:00
0:00
Oct 11 2003
18:00
0:00
Oct 13 2003
Tunø Knob: Nord Pool horizons (init. 08/10/2003 12:00 (GMT), first 12h not in plan)
kW
0
We consider the following methods for estimating the uncertainty of the forecasted wind
power production:
12:00
Oct 9 2003
18:00
0:00
6:00
Oct 10 2003
12:00
kW
0
2000
4000
Tunø Knob: Nord Pool horizons (init. 10/10/2003 12:00 (GMT), first 12h not in plan)
Resampling techniques.
12:00
Ensemble based - but corrected quantiles.
Oct 11 2003
18:00
0:00
6:00
Oct 12 2003
12:00
kW
2000
4000
Tunø Knob: Nord Pool horizons (init. 29/06/2003 12:00 (GMT), first 12h not in plan)
0
Quantile regression.
2000
4000
In many applications it is crucial that a prediction tool delivers reliable estimates (probabilistc forecasts) of the expected uncertainty
of the wind power prediction.
12:00
Stochastic differential eqs.
Jun 30 2003
18:00
0:00
6:00
Jul 1 2003
12:00
kW
0
12:00
Oct 9 2003
18:00
0:00
6:00
Oct 10 2003
12:00
kW
2000
4000
Tunø Knob: Nord Pool horizons (init. 10/10/2003 12:00 (GMT), first 12h not in plan)
0
The plots show raw (top) and corrected (bottom) uncertainty intervales based on ECMEF
ensembles for Tunø Knob (offshore park),
29/6, 8/10, 10/10 (2003). Shown are the
25%, 50%, 75%, quantiles.
2000
4000
Tunø Knob: Nord Pool horizons (init. 08/10/2003 12:00 (GMT), first 12h not in plan)
12:00
Oct 11 2003
18:00
0:00
6:00
Oct 12 2003
12:00
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 16
Quantile regression
A (additive) model for each quantile:
Q(τ ) = α(τ ) + f1 (x1 ; τ ) + f2 (x2 ; τ ) + . . . + fp (xp ; τ )
Q(τ )
Quantile of forecast error from an existing system.
xj
Variables which influence the quantiles, e.g. the wind direction.
α(τ )
Intercept to be estimated from data.
fj (·; τ )
Functions to be estimated from data.
Notes on quantile regression:
Parameter estimates found by minimizing a dedicated function of the
prediction errors.
The variation of the uncertainty is (partly) explained by the independent
variables.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 17
Quantile regression - An example
0
1000
3000
pow.fc
5000
20
25
30
35
2000
1000
0
−2000
25% (blue) and 75% (red) quantiles
2000
1000
0
−2000
25% (blue) and 75% (red) quantiles
2000
1000
0
−2000
25% (blue) and 75% (red) quantiles
Effect of variables (- the functions are approximated by Spline basis
functions):
0
horizon
50
150
250
350
wd10m
Forecasted power has a large influence.
The effect of horizon is of less importance.
Some increased uncertainty for Westerly winds.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 18
Example: Probabilistic forecasts
100
90
80
90%
80%
70%
60%
50%
40%
30%
20%
10%
pred.
meas.
power [% of Pn]
70
60
50
40
30
20
10
0
5
10
15
20
25
30
35
40
45
look−ahead time [hours]
Notice how the confidence intervals varies ...
But the correlation in forecasts errors is not described so far.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 19
Correlation structure of forecast errors
It is important to model the interdependence structure of the prediction errors.
An example of interdependence covariance matrix:
1
40
0.8
35
horizon[h]
30
0.6
25
0.4
20
0.2
15
10
0
5
−0.2
5
10
15
20
25
30
35
40
horizon [h]
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 20
20 40 60 80 100
100%
90%
80%
70%
60%
50%
40%
30%
20%
10%
0
% of installed capacity
Correct (top) and naive (bottom) scenarios
24
20 40 60 80 100
100%
90%
48
80%
72
70%
60%
96
50%
120
40%
30%
144
20%
hours
10%
0
% of installed capacity
0
0
24
48
72
96
120
144
hours
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 21
Types of forecasts required
Basic operation: Point forecasts
Operation which takes into account asymmetrical penalties on deviations from the
bid: Quantile forecasts
Stochastic optimisation taking into account start/stop costs, heat storage, and/or
’implicit’ storage by allowing the hydro power production to be changed with wind
power production: Scenarios respecting correctly calibrated quantiles and auto
correlation.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 22
Wind power – asymmetrical penalties
The revenue from trading a specific hour on NordPool can be expressed as
PS × Bid +
(
PD × (Actual − Bid)
PU × (Actual − Bid)
if
if
Actual > Bid
Actual < Bid
PS is the spot price and PD /PU is the down/up reg. price.
The bid maximising the expected revenue is the following quantile
E[PS ] − E[PD ]
E[PU ] − E[PD ]
in the conditional distribution of the future wind power production.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 23
Wind power – asymmetrical penalties
It is difficult to know the regulation prices at the day ahead level – research into
forecasting is ongoing.
The expression for the quantile is concerned with expected values of the prices – just
getting these somewhat right will increase the revenue.
A simple tracking of CD and CU is a starting point.
0.8
0.4
0.0
Quantile
The bids maximizing the revenue during the period September 2009 to March
2010:
2009−09−01
Monthly averages
2009−11−01
Operational tracking
2010−01−01
2010−03−01
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 24
Value of wind power forecasts
Case study: A 15 MW wind farm in the Dutch electricity market, prices and
measurements from the entire year 2002.
From a phd thesis by Pierre Pinson (2006).
The costs are due to the imbalance penalties on the regulation market.
Value of an advanced method for point forecasting: The regulation costs are
diminished by nearly 38 pct. compared to the costs of using the persistance
forecasts.
Added value of reliable uncertainties: A further decrease of regulation costs – up to
39 pct.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 25
Balancing wind by varying other production
0.20
0.00
0.10
Density
0.20
0.10
0.00
Density
0.30
Naive
0.30
Correct
−10
−5
0
5
10
Storage (hours of full wind prod.)
−10
−5
0
5
10
Storage (hours of full wind prod.)
(Illustrative example based on 50 day ahead scenarios as in the situation considered before)
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 26
Solar Power Forecasting
Same principles as for wind power ....
Developed for grid connected PV-systems mainly installed on rooftops
Average of output from 21 PV systems in small village (Brædstrup) in DK
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 27
Method
Based on readings from the systems and weather forecasts
Two-step method
Step One: Transformation to atmospheric transmittance τ with statistical clear sky
model (see below). Step Two: A dynamic model (see paper).
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 28
Example of hourly forecasts
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 29
Solar Power and Electric Heating (House)
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 30
Conclusions
Some conclusions from more that 15 years of wind power forecasting:
The forecasting models must be adaptive (in order to taken changes of dust on blades,
changes roughness, etc. into account).
Reliable estimates of the forecast accuracy is very important (check the reliability by
eg. reliability diagrams).
Use more than a single MET provider for delivering the input to the wind power
prediction tool – this improves the accuracy with 10-15 pct.
It is advantegous if the same tool can be used for forecasting for a single wind farm, a
collection of wind farms, a state/region, and the entire country.
Use statistical methods for phase correcting the phase errors – this improves the
accuracy with up to 20 pct.
Estimates of the correlation in forecasts errors important.
Forecasts of ’cross dependencies’ between load, wind and solar power might be of
importance. Will be tested on Bornholm in cooperation with CET at DTU Elektro.
Almost the same conclusions hold for solar power forecasting.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 31
Some references
H. Madsen: Time Series Analysis, Chapman and Hall, 392 pp, 2008.
H. Madsen and P. Thyregod: Introduction to General and Generalized Linear Models, Chapman
and Hall, 320 pp., 2011.
P. Pinson and H. Madsen: Forecasting Wind Power Generation: From Statistical Framework to
Practical Aspects. New book in progress - will be available 2012.
T.S. Nielsen, A. Joensen, H. Madsen, L. Landberg, G. Giebel: A New Reference for Predicting
Wind Power, Wind Energy, Vol. 1, pp. 29-34, 1999.
H.Aa. Nielsen, H. Madsen: A generalization of some classical time series tools, Computational
Statistics and Data Analysis, Vol. 37, pp. 13-31, 2001.
H. Madsen, P. Pinson, G. Kariniotakis, H.Aa. Nielsen, T.S. Nilsen: Standardizing the performance
evaluation of short-term wind prediction models, Wind Engineering, Vol. 29, pp. 475-489, 2005.
H.A. Nielsen, T.S. Nielsen, H. Madsen, S.I. Pindado, M. Jesus, M. Ignacio: Optimal Combination
of Wind Power Forecasts, Wind Energy, Vol. 10, pp. 471-482, 2007.
A. Costa, A. Crespo, J. Navarro, G. Lizcano, H. Madsen, F. Feitosa, A review on the young history
of the wind power short-term prediction, Renew. Sustain. Energy Rev., Vol. 12, pp. 1725-1744,
2008.
J.K. Møller, H. Madsen, H.Aa. Nielsen: Time Adaptive Quantile Regression, Computational
Statistics and Data Analysis, Vol. 52, pp. 1292-1303, 2008.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 32
Some references (Cont.)
P. Bacher, H. Madsen, H.Aa. Nielsen: Online Short-term Solar Power Forecasting,
Solar Energy, Vol. 83(10), pp. 1772-1783, 2009.
P. Pinson, H. Madsen: Ensemble-based probabilistic forecasting at Horns Rev. Wind
Energy, Vol. 12(2), pp. 137-155 (special issue on Offshore Wind Energy), 2009.
P. Pinson, H. Madsen: Adaptive modeling and forecasting of wind power fluctuations
with Markov-switching autoregressive models. Journal of Forecasting, 2010.
C.L. Vincent, G. Giebel, P. Pinson, H. Madsen: Resolving non-stationary spectral
signals in wind speed time-series using the Hilbert-Huang transform. Journal of
Applied Meteorology and Climatology, Vol. 49(2), pp. 253-267, 2010.
P. Pinson, P. McSharry, H. Madsen. Reliability diagrams for nonparametric density
forecasts of continuous variables: accounting for serial correlation. Quarterly
Journal of the Royal Meteorological Society, Vol. 136(646), pp. 77-90, 2010.
G. Reikard, P. Pinson, J. Bidlot (2011). Forecasting ocean waves - A comparison of
ECMWF wave model with time-series methods. Ocean Engineering in press.
C. Gallego, P. Pinson, H. Madsen, A. Costa, A. Cuerva (2011). Influence of local
wind speed and direction on wind power dynamics - Application to offshore very
short-term forecasting. Applied Energy, in press
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 33
Some references (Cont.)
C.L. Vincent, P. Pinson, G. Giebel (2011). Wind fluctuations over the North Sea.
International Journal of Climatology, available online
J. Tastu, P. Pinson, E. Kotwa, H.Aa. Nielsen, H. Madsen (2011). Spatio-temporal
analysis and modeling of wind power forecast errors. Wind Energy 14(1), pp. 43-60
F. Thordarson, H.Aa. Nielsen, H. Madsen, P. Pinson (2010). Conditional weighted
combination of wind power forecasts. Wind Energy 13(8), pp. 751-763
P. Pinson, G. Kariniotakis (2010). Conditional prediction intervals of wind power
generation. IEEE Transactions on Power Systems 25(4), pp. 1845-1856
P. Pinson, H.Aa. Nielsen, H. Madsen, G. Kariniotakis (2009). Skill forecasting from
ensemble predictions of wind power. Applied Energy 86(7-8), pp. 1326-1334.
P. Pinson, H.Aa. Nielsen, J.K. Moeller, H. Madsen, G. Kariniotakis (2007).
Nonparametric probabilistic forecasts of wind power: required properties and
evaluation. Wind Energy 10(6), pp. 497-516.
Vind i Øresund Workshop at IEA, LTH, September 2011 – p. 34